error code SEIC-F1040-535-04

Not sure what that error code is. What is the description?

Having twins on the return is not the cause of this rejection.  The return was rejected because the SSN and the date of birth for either or both of these children as reported on Sch EIC do not match the IRS' records.

You should check the dob and SSN against these children's birth certificates and social security cards.

If you determine these to be correct as shown on the return, your client should call the SSA to verify their records, which may require correction.  Any change may take 10 business days before it will be reflected on the IRS' system.

In the even everything is correct but the return still cannot be e-filed, the only option would be to paper file the return with a F.8948

Were they born in December?  I remember one year there was a delay in issuing cards, and therefore in SSA making the data available to IRS.  Also, ask to see the cards.  Remember these clients are dealing with twins 24/7.